Flanked by two publicists, immaculate enough to stop conversation dead, Priyanka Chopra takes a seat in a Manhattan hotel bar, removes her super-size sunglasses and in a hoarse, post-party voice asks for room-temperature water and a lemon and honey tea. She is every inch the superstar, even in a country where she isn't.

In India, Chopra is a national icon. A former Miss World – she won the contest in 2000, at the age of 18 – she has gone on to become one of the highest-paid actors in Bollywood. Now she is rebranding as an international pop star.

"I grew up in America for a while," the 31-year-old explains. "I went to high school here for five years. I don't remember seeing anyone who looked like me or that I could look up to. And now the world is becoming such a small place, the girl next door could be from anywhere. That's what I want to champion. I want to break the mould."

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There is certainly faith that she will: Chopra is signed to Interscope, home to Madonna, Lana Del Rey and M.I.A. Her 2012 single In My City featured will.i.am; the follow-up, Exotic, roped in Pitbull. Her third and current single, a cover of Bonnie Raitt's I Can't Make You Love Me, is her first fully solo pop outing – but behind the scenes "Team PC", an army of 28 employees, she says, working for her in LA and Mumbai, have enlisted RedOne to produce her debut album, due later this year. He has previously worked with the likes of Lady Gaga and Jennifer Lopez. Labelmate Dr Dre, meanwhile, is using her song in his new advert for Beats by Dre.

"I'm an entertainer," Chopra says in sing-song. "I'm born to go anywhere in the world and make you laugh and make you dance, make you sing. Busy is the new happy." That's her mantra when you ask her about her intense workload – she shot four films, promoted two more, plus recorded some 40 tracks for her album last year, when her father died of cancer. "I started shooting Mary Kom [her forthcoming biopic of the Indian boxer] four days after he died, and it was incredibly difficult ... but I had to channel it. Boy, did I channel it." She shows me pictures of her boxing on set, bulging and ripped. "Hours of training in the gym every day…" She shakes her head. "I can't tell you how happy I am that shoot is over."

Her movie career has been surprisingly eclectic: she has routinely mixed up blockbuster parts with acclaimed indie fare, starring in India's first superhero franchise (the Krrish series) in the year she played an autistic runaway (Barfi!). She won a National Film award – India's equivalent of an Oscar – in 2008 for Fashion, in which she portrayed an exploited model.

Chopra is keen on breaking stereotypes of Indians in the US: "We don't talk like Apu from The Simpsons, and there's more to the world's biggest democracy than henna and sparkly clothes." At the same time, she insists, she is a citizen of the world. The weekend before we meet, Chopra was given a "woman of substance" award at the International Indian Film awards – "because of my philanthropy, I guess. And because I'm cool."

"And modest," chips in one of her publicists. She isn't, of course: Chopra is entertainingly matter of fact about her beauty, intelligence and talent.

Her IIFA highlight was dancing on stage with John Travolta. "We partied! He was so great; we danced his Pulp Fiction moves spontaneously, totally unrehearsed." She also hosted an acting masterclass, unfazed that her partner on the panel was Kevin Spacey.

"It's my fans who have the most impact on me," she says, telling me about the last time she was caught off-guard. "There was a crowd of people waiting outside after a party in New York. I made a point of meeting them and this one [Indian] girl, around 14, ran up crying and hugging me, frozen because it was so cold. I said, 'What happened? Are you OK?' And she said: 'Thank you. Thank you for making us relevant.' That's a huge line, huge words. I never thought I was capable of that."

• Priyanka Chopra has partnered with Nokia MixRadio to curate her personal MixRadio playlists, allowing fans in 31 countries to discover music from across the globe. mixrad.io.